G.LO.08.02 Find the distance between two points on the coordinate plane using the distance formula; recognize that the distance formula is an application of the Pythagorean Theorem. Solve problems about geometric figures
METS-S/NETS-T
NET: 2.b. Communicate information and ideas effectively to multiple audiences using a variety of media and formats
Essential Questions:
What is the distance formula? When can you use it?
Objectives:
With a group of peers, students must build an iMovie using slides and outlining Pythagreon theorem. Students must include at least two example equations.
Tools and Resources:
camera
microphone
youtube (for upload)
props
storage device for computer (if needed)
Rationale:
The Pythagorean Theorem as well as the distance formula are used throughout all math courses after Geometry. By having the students create a jingle to help them remember the formula, it will help them to remember it easier. By having the students work together to create something that embodies them, they will be more motivated to understand the theorem and participate in examples.
Sequence of Activities:
Anticipatory Questions/Activity:
Say you want to listen to some music while you are doing your homework tonight, but you don’t have your headphones. Instead, you have to use speakers. The ultimate question, how far apart do you have to place the speakers from one another, so that both of your ears enjoy the perfect listening experience?
Body of Lesson Plan: Segment #1 (Artifact: link to real world, website, book, picture, etc.)
Given certain points: (1,2) and (3,4) and (3,2) As well as lengths: 2 and 2 The teacher will label and show students the following link and ask how they would be able to answer the lessons opening question:
Segment #2 (Factual information/Vocab Includes sample feedback loop)
More than likely, the students will tell the teacher that they can solve the problem using work from their last lesson. The Pythagorean Theorem can be used with the 2s. set up like this 2²+2²= c² Then ask what the distance would be? 2√2 Then ask the question, how else do you think we could solve this problem? If no one answers, ask the students to take out a piece of grid paper and plot A=(1,2) B=(3,4) and C=(3,2) Have them count the lengths of each side using the graph paper. And ask if they didn’t have have lengths, what two points would they use if they were to plug it into the Pythagorean theorem. Points A and B Then ask what they need to do in order to make it one number for the a and b in a²+b²=c² Subtract x values and y values in the same order (x1-x2) and (y1-y2) and then square both subequations. Finally, ask what you would do to both sides of the Pythagorean Theorem to get c by itself Square both sides. So by manipulating the Pythagorean Theorem students create the distance formula, which finds the distance between two points. Which should look like this d=√((x1−x2)2+(y1−y2 ))2
Based off the opening sample have the students break off into small groups. Each group should create one real-life application of how to use the distance formula as well as two examples using points and graph paper. Each member of the group should be able to solve the problem. Once a group believes they have three SOLID examples, they must have the teacher check work for accuracy.
Segment #4 (Detailed directions on how to complete activity)
After completing segment three, Students will be asked to create an iMovie
They must have at least 2 approved examples to show in the video
The video must be at least 3 minutes long
Students will use the iMovie application to create video
Each member of the group must participation and be given credit in some part of the video
Each group must be no larger than 3-4 students
Video must include detailed working of the problem
Video must have visual aid of the problems
Students will present in front of class
Students will be given 2 days to complete the video
Name:Justine Lakosky_
microphone
youtube (for upload)
props
storage device for computer (if needed)
Segment #1
(Artifact: link to real world, website, book, picture, etc.)
As well as lengths: 2 and 2
The teacher will label and show students the following link and ask how they would be able to answer the lessons opening question:
http://www.vernier.com/images/cache/lab.RWC-LP-14-from_here_to_there.305.238.png
(Factual information/Vocab
Includes sample feedback loop)
The Pythagorean Theorem can be used with the 2s. set up like this 2²+2²= c²
Then ask what the distance would be?
2√2
Then ask the question, how else do you think we could solve this problem?
If no one answers, ask the students to take out a piece of grid paper and plot A=(1,2) B=(3,4) and C=(3,2)
Have them count the lengths of each side using the graph paper. And ask if they didn’t have have lengths, what two points would they use if they were to plug it into the Pythagorean theorem.
Points A and B
Then ask what they need to do in order to make it one number for the a and b in a²+b²=c²
Subtract x values and y values in the same order (x1-x2) and (y1-y2) and then square both subequations.
Finally, ask what you would do to both sides of the Pythagorean Theorem to get c by itself
Square both sides.
So by manipulating the Pythagorean Theorem students create the distance formula, which finds the distance between two points. Which should look like this
d=√((x1−x2)2+(y1−y2 ))2
(Includes multiple intelligence strategy:
Hands-on, small groups, reteaching strategy)
(Detailed directions on how to complete activity)
SAMPLE OF iMovie link follows.
http://youtu.be/k9q3KObgWGI
Embedded video is presented at the end.